ABSTRACT
The complexity of action is what motivates the recourse to mathematics, allowing the construction of a simplified model of it, thus to make it intelligible, and, at the same time, it is what creates the difficulty in applying this to undertaking. Because of its formal characteristic, mathematics has at its disposal the capacity to bring into light the logical structure of action, in other words, to arrange and state in a hierarchical system the parameters which constitute it and to study the relations between them. Thus a first outline appears which distinguishes the approach undertaken by mathematics of action from that which is suitable to mathematics of nature or mathematics of engineering. The confrontation of mathematics of action and experience then concerns firstly the possible experience which alone has the effective capacity to validate or invalidate the model, since it alone is susceptible to be adequate for the model.
